Methods and apparatus for solving mathematical problems for entertainment

ABSTRACT

A game including a game board with a game travel path defined thereon, a game token moveably placeable on the game travel path, and a move generator associated with the game comprising numbers, mathematical operators, mathematical operations, variables, and variable values. A method of constructing a move includes forming the mathematical expression components into a mathematical expression to yield a movement value, and then moving the game token along the game travel path according to rules of the game for the movement value.

BACKGROUND OF THE INVENTION

The present invention relates to methods and apparatus for solving mathematical problems. In another aspect, the present invention relates to methods and apparatus for solving mathematical problems for entertainment purposes. In still another aspect, the present invention relates to educational and instruction methods and apparatus for teaching and/or learning mathematical concepts.

There are a number of U.S. Patents that relate to mathematics games, the following of which are merely a few.

U.S. Pat. No. 5,033,754, issued Jul. 23, 1991, to Finch, discloses a card game apparatus and method of play, involving the systematic solution of algebraic equations. The apparatus includes an algebraic equation and a set of cards having indicia denoting the mathematical operations of “multiply”, “divide”, “add X's”, “subtract X's”, “add constant”, and “subtract constant”. Players are dealt cards and take turns modifying the equation by performing mathematical operations directed by cards they hold. The person who solves the equation is the winner. Play money may be used to keep score.

U.S. Pat. No. 5,318,447, issued Jun. 7, 1994, to Mooney, discloses an educational game for teaching arithmetic, which includes a game board having a travel route divided into segments, at least one arithmetic problem printed within each of at least some of the segments, several individual game tokens, each token for marking a player's location along the travel route, a chance control device for determining the extent of a single movement of each token, and an answer card providing the solution to the at least one arithmetic problem, and is offered at several levels of difficulty. A method of playing this educational game is provided, where several players take turns, one turn including the steps of a player activating the chance control device and advancing a token along the travel path a number of segments as indicated by the chance control device, offering a solution to any arithmetic problem contained within the segment on which the token comes to rest after being so advanced, comparing the solution to the correct solution appearing on the answer card, keeping the token on the segment if the offered solution matches the solution appearing on the answer card, and moving the token backward at least one segment along the travel route if the offered solution fails to match the solution appearing on the answer card.

U.S. Pat. No. 5,445,390, issued Apr. 29, 1995, to Dutton et al., discloses a mathematical Board Game for a plurality of players, which has a rectangular game board with a plurality of card stations or chambers arranged in a matrix of horizontal and vertical rows. The card chambers include a start card chamber in each corner of the board and a plurality of problem card chambers in a perimeter of the board between the start card chambers. A plurality of answer card chambers on the board are surrounded by the start card chambers and the problem card chambers. A start card is removably placed in each of the start card chambers. A problem card is removably placed in each one the problem card chambers. There is a different mathematical problem on each problem card. An answer card is removably placed in each one the answer card chambers. There is an answer to one of the mathematical problems on each of the answer cards. A plurality of position tokens is removably and selectively placed on the start cards and on the problem cards to assist the players in keeping track of their and other player's moves. A set of dice are thrown and placed on the board to randomly select which player of the plurality of players will move one of the position tokens before another player moves another one of the other position tokens. Each player takes his or her turn in that order until the game is finished.

U.S. Pat. No. 6,308,955, issued Oct. 30, 2001, to Slatter, discloses a mathematical board game for 2 to 8 players, invented primarily for beginners and individuals struggling with the four basic formats of mathematics. The banker is allocated by use of a spinner, players then determine who moves first, by use of this spinner, and in which of the four formats they will play, these are: Subtraction, Multiplication, Addition and Division. Players then move by taking four steps. (1) Taking a question card out of the appropriate question bag; (2) Working out the relevant sum; (3) Looking up the answer on the correlating Answer Value Chart, which converts the answer of the mathematical sum to a given value, which is a number; (4) Moving that number of spaces on the board and receiving that amount of money from the bank. The board's defined numbered travel path is from 1 to 144 spaces. Some spaces are marked with various symbols, which require various actions that affect the players. Players move their playing piece horizontally from left to right, right to left, to a Finish Award they have nominated, which conveniently gives players the choice of a quick, medium or lengthy game. The Answer Value Charts enables the three sections; Sub-Junior, Junior and Senior—players of varying ages and abilities, to play together, with an equal chance of achieving equal values. The winner is the player with the most money on completion, thereby winning by chance not academically. Other known facts incorporated, enable every player to attain the correct answers, while facilitating their personal learning styles.

U.S. Pat. No. 6,554,280, issued Apr. 29, 2003, to Mazzola, discloses an ant game, where a player's knowledge of mathematical relationships are applied, including greater than, less than, odd number or even number relationship, or a combination thereof. The game board has start and end spaces, sequentially disposed game spaces arranged therebetween, an ant cave arranged next to one sequentially disposed game space, an ant tunnel connecting one sequentially disposed game space and another non-adjacent sequentially disposed game space so that a player whose token lands on the first sequentially disposed game space may move across the ant tunnel to a given sequentially disposed game space located on the other side of the ant tunnel, and a move-to-ant-cave indicator on some sequentially disposed game spaces indicating that a player whose token lands thereon is to go to the ant cave.

U.S. Pat. No. 6,648,648, issued Nov. 18, 2003, to O'Connell, discloses an educational game for teaching mathematics, which has a game board with a continuous play path along its edge. Spaces are labeled with a mathematical category and a monetary amount. Each mathematical category has its own deck of cards with questions, answers and explanations. At least one of the spaces of the game board is labeled with the help category. When a player lands on this space they receive a help card, which permits that player to ask another player for help in solving a question. The game is played by moving a marker along the play path. If the marker stops on a space that has a mathematical category the player selects corresponding card. If the player's solution to the question and answer on the card match the player collects play money in the amount printed on the space. If not, play proceeds to the next player and the first player continues to work on the question, giving that player the ability to self-correct. All solutions may be collected as an assignment by a teacher in a classroom setting. The first player to accumulate a specified amount of play money is the winner.

SUMMARY OF THE INVENTION

According to one embodiment of the present invention, there is provided a game comprising a game board, a game travel path defined on the game board comprising a number of spaces, a game token moveably placeable on the game travel path, and a move generator associated with the game comprising numbers, mathematical operators, variables, and variable values.

According to another embodiment of the present invention, there is provided a method for moving of a game token along a game travel path the method comprising selecting mathematical expression components from the group consisting of numbers, mathematical operators, variables and variable values, forming the mathematical expression components into a mathematical expression to yield a movement value, and moving the game token along the game travel path according to rules of the game for the movement value

According to even another embodiment of the present invention, there is provided a game having a game environment, a move generator associated with the game comprising numbers, mathematical operators, mathematical operations, variables, and variable values, wherein the move comprises any change in the game environment.

According to still another embodiment of the present invention, there is provided a method for moving of a game token along a game travel path. The method includes selecting mathematical expression components from the group consisting of numbers, mathematical operators, mathematical operations, variables and variable values. The method further includes forming the mathematical expression components into a mathematical expression to yield a movement value. The method even further includes moving the game token along the game travel path according to rules of the game for the movement value.

According to yet another embodiment of the present invention, there is provided a method for producing a move in an entertainment game having a game environment. The method includes selecting mathematical expression components from the group consisting of numbers, mathematical operators, mathematical operations, variables and variable values. The method further includes forming the mathematical expression components into a mathematical expression to yield a movement value. The method even further includes implementing a move corresponding to the movement value to effect the game environment. A further embodiment of this embodiment is provided wherein the move corresponds to changes in the game environment comprising changing position, size, shape, coloration, or pattern of a visual feature, changing pitch, duration, volume, harmony, or pattern of sound, changing pressure, temperature, or texture, changing aroma, noxiousness, intensity, duration, or changing taste, bitterness, sweetness, sourness, acidity, intensity, or duration. An even further embodiment of this embodiment is provided wherein the move corresponds to changes in the game environment comprising creating, eliminating, changing, revealing “hidden” states. A still further embodiment of this embodiment is provided wherein the move corresponds to changes in the game environment comprising providing stimulus to effect mental or emotional state of a game player.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of game board 100 of the present invention, having thereon, a plurality of spaces 119, including go space 101, non-event spaces 103, monetary loss spaces 105, monetary gain spaces 106, workout card spaces 108, and delineated counter spaces 111, all of which collectively define continuous travel path 120, with positive direction defined in the direction of arrows 110, and having thereon, workout card position 116, and variable card position 116.

FIG. 2 is an illustration showing number tiles 125, which have either positive or negative integers thereon, and may include exponents.

FIG. 3 is an illustration showing operation tiles 130 which have printed on them symbols of +, −, ×, or /, for addition, subtraction, multiplication and divisional, respectively.

FIG. 4 is an illustration showing parenthesis tiles 140, which depending upon their orientation are either left or right parenthesis.

FIG. 5 is an illustration showing player tokens 150, each unique and used to represent each player, in travel along travel path 120.

FIG. 6 is an illustration showing variable tiles 160, which in the illustrated embodiment are the variables a, b, x, y, m, and n.

FIG. 7 is an illustration of one variable card 185 from the variable card deck, and it contains a listing of one or all of the variables, and provides possible numbers for the variable.

FIG. 8 is an illustration of a workout card 188 from the workout card deck, containing a mathematical problem to solve and a monetary reward for a correct solution.

FIG. 9 is an illustration of money 180 of various denominations.

FIG. 10 is an illustration of optional timer 195, which may be optionally utilized to provide a time limit for completing a turn, or for completing a workout card 188.

DETAILED DESCRIPTION OF THE INVENTION

According to the present invention, there is provided a method of generating a value to effect a move in a game, with the player selecting from among numbers, mathematical operators, mathematical operations, variables, and values for variables to construct a mathematical expression that yields a desired value to effect a desired move. Thus, unlike random games of chance in which a player is provided a random value from a dice roll, spinner, and the like, and must accept the resultant random value, with the present invention, a player may envision a desired move and then construct a suitable mathematical expression that yields a desired value that produces the desired move.

It should be understood that many of the terms used herein have certain and definite meanings to mathematicians and those of skill in mathematics.

A mathematical operator is just a function from a set to itself. Non-limiting examples of common operators useful in this invention include numbers and vectors. A mathematical operation is a function that maps one or more things in a set back into the same set. Non-limiting examples of common operations useful in this invention include negation, addition, subtraction, multiplication, and division.

As used in this invention, numbers will be considered mathematical operators. Game complexity can be controlled through the use of vectors as a mathematical operator. For example, 2 dimensional vectors can be used to effect position on a surface/plane, and 3 dimensional vectors can be used to effect position in space. Vectors can also be used to effect changes with respect to time. Vectors can also be used to effect all sorts of changes to the game environment, including those discussed below. It should also be understood that mathematical operators can also include any conceivable mathematical expression

It should be understood that a move is preferably the traditional movement of a game piece on a game board (whether an actual physical board, or virtual computer generated board displayed on a computer screen, or displayed thru game goggles or helmet, or projected into the air such as a holograph), but may generally also include any action that causes a change in the state of the game playing region or board (i.e., a change in the game environment). A change in the game environment may entail changing physically recognizable states, which for sight includes position, size, shape, coloration, pattern of a visual feature, for hearing includes pitch, duration, volume, harmony, pattern of sound, for touch includes pressure, temperature, texture, for smell, includes aroma, noxiousness, intensity, duration, and for taste includes taste, bitterness, sweetness, sourness, acidity, intensity, duration. Changes in the game environment may also include creating, eliminating, changing, revealing “hidden” states, for example, setting traps unknown to opponents or opening favorable, hidden paths for future use, etc. Changes in the game environment may also include influencing mental or emotional states of the players thru use of stimulus as desired.

One embodiment of the present invention will now be described by reference to the Figures. In this embodiment, the game comprises a game board 100, number tiles 125, operation tiles 130, variable tiles 160, parenthesis tiles 140, player tokens 150, variable cards 185, workout cards 188, money 180, and an optional timer.

Referring first to FIG. 1, there is shown game board 100 of the present invention, having thereon, a plurality of spaces 119, including go space 101, non-event spaces 103, monetary loss spaces 105, monetary gain spaces 106, workout card spaces 108, and delineated counter spaces 111, all of which collectively define continuous travel path 120, with positive direction defined in the clockwise direction by arrows 110, and having thereon, workout card position 115, and variable card position 116.

It should be understood that the present invention is not meant to be limited to the embodiment as shown in FIG. 1, and that everything about game board 100 (i.e., size, shape, color, arrangement), may be changed as desired as long as the basic tenets of the game of the present invention are substantially followed. It is also contemplated that the present invention finds utility with computer implemented games (whether the computer is a general purpose programmable computer, or a dedicated game device).

Accordingly, any suitable shape of game board 100 may be utilized, including any desired regular or irregular geometric shape, any desired regular or irregular polygon of any number of sides, or any shape having a curvilinear perimeter. While game board 100 is shown as a 2-dimensional board having a playing surface in a single plane, it should be understood that game board 100 may comprise multiple playing surfaces in multiple planes, may comprise a 3-dimensional playing surface (i.e., as a simple non-limiting example, steps may be included in travel path 120). Game board 100 may also include a plurality of boards with one or more travel paths 120 linking play between the various boards. Such a multiplicity of boards may be positioned in the same plane (i.e, laid upon a table surface or the floor), or the multiplicity of boards may be arranged in various planes (i.e., in a manner such as a 3-d chess game).

Further accordingly, it should be understood that any desired number, shape, color and size of spaces 119, may be utilized to construct travel path 120. While travel path 120 is shown as a continuous loop, it should be understood that travel path may include more than one loop, may include a number of side paths, dead-ends, or detours, may include short-cuts or paths across the loop, and instead of a continuous loop, may comprises a non-loop path from a starting point to an ending point.

Even further, the number and arrangement of the various specific spaces (i.e., go square 101, non-event squares 103, monetary loss/gain squares 105/106, workout squares 108, and counter spaces 111, may be varied as desired. That is, game board 100 may include more or less of any of these specific squares, provided that the resulting game board 100 may allow for substantial operation of the basic tenets of the game of the present invention. For example, multiple go spaces could designate multiple starting points, perhaps a unique one for each player, perhaps a unique one depending upon circumstances, or perhaps it's just another choice given a player.

It should also be understood that the present game is not limited to any particular monetary value on any of the spaces, or cards, but rather any desired monetary value may be utilized. It should also be understood that game board 100 may also include other types of penalty/reward spaces, other types of card-drawings spaces, or any other types of spaces as may be envisioned for a board game.

The size and arrangement of workout card position 115, and variable card position 116 are also not critical. While it is preferred to have workout and variable card positions 115 and 116 defined on game board 100, it is also possible to provide that workout and variable cards be positioned off of game board 100, either in a stand alone holder(s), or without a holder. Finally, in a loop arrangement, the direction of arrow 110 is not critical and may be used to define a positive or negative direction. With a non-loop travel path from starting point A to finish point B, it is most convenient to follow a logical arrangement, and let arrow 110 denote positive direction travel from point A to point B, but even that is open to change.

Referring additionally to FIG. 2, there are shown number tiles 125, which have either positive or negative integers thereon, and may include exponents. For example, 1, (−1), 4, 5² and the like. While the embodiment as shown in FIG. 2 only utilizes integers ranging from −5 to 5 any suitable range of numbers, which may or may not be symmetric around zero, may be utilized. And, while mostly lower exponents are utilized to minimize difficulty, certainly a more challenging embodiment would be to utilize higher exponents.

Referring additionally to FIG. 3, there are shown operation tiles 130 which have printed on them symbols of +, −, ×, or /, for the commonly known mathematical operations of addition, subtraction, multiplication and divisional, respectively (certainly, other commonly used symbols, such as “*” for multiplication and “÷” for division may be utilized). Of course, any other mathematical operator may be utilized, non-limiting examples of which include, an exponent, a root, modulo, reciprocal, an absolute value, truncation, rounding, ±(to allow a player to choose between the positive or negative value of the number), and the like. For example, if a tile with an arrow where utilized, then arranging the tile with the arrow pointing upward could represent raising a number to an exponent, while arranging the tile with an arrow pointing downward could represent taking a root of a number.

Referring additionally to FIG. 4, there are shown parenthesis tiles 140, which depending upon their orientation are either left or right parenthesis.

Referring additionally to FIG. 5, there are shown player tokens 150. Each token 150 is unique and is used to represent each player, in travel along travel path 120. Of course, size, shape and color are selected as desired provided token 150 can be accommodated on game board 100.

Referring additionally to FIG. 6, there are shown variable tiles 160. In this embodiment, variables a, b, x, y, m, and n are utilized. Of course, it should be understood that any desired number of variables may be utilized. While any suitable type of variable representation may be utilized, for example, a circle, square, diamond, dot, stick figures, apples, oranges, or any other pictorial representation, it is generally preferred to utilize variables as are commonly encountered in math, physics and engineering, which are typically about any alphabetic character and/or Greek characters.

Referring additionally to FIG. 7, there is shown one variable card 185 from the variable card deck. Variable card 185 contains a listing of one or all of the variables, and provides possible numbers for the variable. For example, variable a can have a value of −3, −1 or 0, as desired by the player. Of course, it is possible to have game modifications, where your opponent declares which value you must use, or perhaps a game modification where you use the first value, the last value, or an average value, or any other conceivable modification. The values for the variables may also be provided by a random number generator, dice, spinning wheel, or by drawing various numbers. Another play variation is also contemplated in which the player first builds a mathematical expression containing one or more variables, and with the variable then randomly generated after creation of the expression.

Referring additionally to FIG. 8, there is shown a workout card 188 from the workout card deck. Generally, a workout card 188 will have a mathematical problem to solve and a monetary reward for a correct solution. Workout cards 188 may vary in difficulty, with each player using cards matched to that player's ability. For example, there could be workout cards 188 correlated to grade/ability level, and each player would select a card from the deck of that player's grade/ability level. This provides an easy method of handicapping the play so that players of different levels may play competitively. There could also be themed cards, that is, as non-limiting examples, math problems having a basis in physics, statistics, chemistry, biology, cooking, history, sports, economics, business, shopping, music, travel, and weather. Card difficulty may be indicated thereon by any manner or scheme that will convey the difficulty, non-limiting examples of which include, a color scheme, a number scheme, an alphabetic scheme, an alphanumeric scheme, reference to school grades, reference to military ranks, reference to royalty ranks, or a reference incorporating the theme of the card (for example, cooking cards could use fruits, or foods). A two-fold pedagogical benefit also occurs: lower level players watch higher level players work their problems and learn how to do them, and the higher level players review their knowledge by watching lower level players work their problems.

Referring now to FIG. 9, there is shown money 180 of various denominations. The number and type of currency is not critical to the present invention.

Referring now to FIG. 10, there is shown an optional timer 195, which may be optionally utilized to provide a time limit for completing a turn, or for completing a workout card 188. While timer 195 is shown as a familiar kitchen-type analogue-type of timer, one or more hourglasses with sand, or a digital timer may be utilized. Such a timer may be incorporated into game board 100, or may stand alone. As another method of making play competitive between players of varying ability, more time could be provided to players of lesser ability, and less time to those of more ability.

One non-limiting example of a game embodiment of the present invention is played as follows.

At the start each player gets a designated amount of money. Both the Workout and Variable decks should be adequately shuffled. In one bag (or container) are placed number tiles 125 and variable tiles 160, and into another bag (or container) are placed operation tiles 130. Alternatively, rather than using a bag/container, these tiles may be segregated into a first pile or location, and a second file or location

To determine order of play, each player draws a number tile (if variable tile is drawn, draw again). The player nearest to 0 goes first, keeping in mind that 1 and −1, 2 and −2, etc, are equally close to zero. In the event of a tie for closest to 0, those tying redraw until only one player is closest to 0.

Starting with the first player, going around to the left, each player draws a designated number of number/variable tiles, which in this embodiment is 4, and a designated number of operation tiles, which in this embodiment is 3. Next, in clockwise order, each player sets their token on go space 101 constructs a number, and moves their token according to the movement rules.

If a player's token is off the board, the player places it on GO. In this game, moves are made by either playing a number tile having a number that is the desired number of moves or by constructing an expression yielding a number that is the desired number of moves, with a positive number moving token 150 in the direction of arrows 110, and a negative number moving token 150 against the direction of arrows 110.

The negation operation, −, always reverses the direction of the number following it. For example, playing

will move token 150 backward 3 steps in the opposite direction of the arrows (counter-clockwise), and

will move token 150 three steps forward.

Addition of two numbers moves token 150 by one of the numbers first and then by the other number. For example

-   -   moves token 150 forward 2 steps and then forward another 3 steps         for a total of 5 steps. The player could just as well move 3         steps and then 2 steps since 2+3=3+2=5.

If the tiles

are played, the player could move 2 steps backward and then 3 steps forward or 3 steps forward and then 2 steps backward for a total of 1 step forward. Likewise,

moves 2 steps forward and 3 steps back for a total move of 1 step back, and

moves 2 steps back and the 3 more steps back for a total move of 5 steps back.

Subtraction of two numbers is really done by adding the first number to the reverse or opposite of the second number. For example

moves token 150 backward 2 steps and then forward 3 steps, while

moves token 150 2 steps in the opposite direction of −2 and then 3 steps forward. But the opposite direction of −2 is forward. So what actually happens is token 150 is moved 2 steps forward and then another 3 steps forward.

Multiplication of two numbers can be thought of as shorthand for adding the same number several times. For example, 3×2 means 2+2+2. In other words, 3 twos. Thus

moves 2 steps forward three times in a row and

moves 2 steps backward three times in a row. Multiplying by a negative number on the left does the same thing as if it were positive except it reverses the direction. For example

means “reverse the direction of 3×2” and will move token 150 2 steps backward three times in a row. Similarly

means “reverse the direction of 3×(−2)” and will move token 150 2 steps forward three times in a row.

doesn't move token 150 at all so the player can draw another number, replace the 0 and play. However if the player is on a Workout space 108 or Money space 106/105, the player gets to draw another Workout Card 188 or collect/pay money again before continuing to play. In other words, playing a 0 gives the player a free move. If you play a variable tile, say

and your variable card says that x can take on the value 0 and you select this value for x, then x is the number 0 and you can take your free turn.

A free turn does not result from play of an expression such as

which evaluates to 0.

Complex Expressions. An expression such as

moves forward 1+4 steps 3 times and then moves backward 2 steps. Correct punctuation must be used when forming these kinds of expressions. For example, placing two operation symbols next to each other as in 2+−3 is illegal. Such an expression must utilized a pair of grouping symbols 140 as in 2+(−3).

The present embodiment of the game of the present invention utilized the following Rules of Play.

Rule 1. Any time a player's token has been removed from the board and it is that player's turn to play, that player places places a token on go space 101 and plays as usual.

Rule 2. A player must move the number of steps the expression evaluates to, even if the player evaluated it incorrectly.

Rule 3. If a player uses tools other than brain power, a pencil and piece of paper, that player loses a turn.

Rule 4. Playing an improperly formed expression, results in a lost turn. Normally 2(3) and 2x are taken to mean the products 2×3 and 2×x. However, in the present game embodiment, this is not allowed. The multiplication symbol “−”, or “·” must be placed between the two numbers.

Rule 5. After a player's move, the player replaces the Number Tiles 125 and Operation Tiles 130 by drawing additional tiles from the tile bags, and then, places the used tiles back in their bags (otherwise that player might draw the tiles just played).

Rule 6. If a player lands on a space marked with a $, that player collects the amount of money shown from the bank.

Rule 7. If a player lands on a space marked with a −$, that pays the amount of money shown to the bank.

Rule 8. If a player lands on a space marked with a

, that player draws a card from the Workout Deck. If that player can correctly answer the question on the card, that player collects the amount of money shown from the bank.

If a first player lands on a space occupied by a second player's token, that player removes the second player's token from the board and receives a designated amount ($50 in this embodiment) from the second player player. If second other player has less than the designated amount, the first player takes all the money the second player has.

In this embodiment, anytime a player makes at least one complete circuit of the board either forward or backward in a single move, that player collects a designated value, which, in the embodiment shown is $50. Playing an expression such as

moves 103 forward steps, resulting in passing the starting space twice. That player collects collects a designated amount ($50 in this embodiment), because it doesn't matter how many circuits are actually made, a flat designated amount is collected. Of course, other embodiments could include collecting the designated amount times the number of circuits.

Variables are to a certain extent wild cards. If a player draws a variable tile such as

and does not have a variable card, that player immediately draws a variable card. If the card drawn looks like variable card 188 shown in FIG. 8, a look at the x-row reveals that “x can be 1, 2, 3, or −4” for xε{1, 2, 3, −4}. Then, when that player plays

That player can choose which value of x desired, meaning that player can make the next move to be

However the value picked for x has to be the same each time x occurs in the expression played. For example for the expression

and choosing x=2, will result in

After a player's turn, if that player has no more variable tiles, that player must return the variable card to the bottom of the deck. If that player still has a variable, that player keeps the card for use on the next turn.

According to the present invention, a timer may be utilized to maintain a desired pace of play. For beginner players, 3 minutes a move generally work for the first few games. Once the players are familiar with the game, 2 minutes and even 1 minute a move is adequate. If a player landed on a Workout square, an additional 3 minutes is sufficient to work the problem.

There are certainly a number of way to play the game, limited only by the imagination.

As a non-limiting example, the first person to accumulate a designated number of dollars wins the game.

As another non-limiting example, the person with the most money when time is called wins the game.

As even another non-limiting example, each player can be given a certain amount of total time for playing, either the same time for each player, or perhaps more time for mathematically weaker player and less time for mathematically stronger players. Time is deducted from a player's total time for time expended on each turn. Players become inactive as they run out of time, with the game ending when all players have run out of time, with the winner being the player with the most accumulated money.

While the illustrative embodiments of the invention have been described with particularity, it will be understood that various other modifications will be apparent to and can be readily made by those skilled in the art without departing from the spirit and scope of the invention. Accordingly, it is not intended that the scope of the claims appended hereto be limited to the examples and descriptions set forth herein but rather that the claims be construed as encompassing all the features of patentable novelty which reside in the present invention, including all features which would be treated as equivalents thereof by those skilled in the art to which this invention pertains.

It should also be understood that while the present invention has been illustrated by reference to being played on a physical board with physical game pieces and money, the present invention also may be played in representative fashion on a computer or game machine. 

1. A game comprising a game board; a game travel path defined on the game board comprising a number of spaces; a game token moveably placeable on the game travel path; a move generator associated with the game comprising numbers, mathematical operators, mathematical operations, variables, and variable values.
 2. The game of claim 1, wherein the move generator comprises number cards, mathematical operator cards, mathematical operation cards, variable cards, and variable value cards.
 3. The game of claim 1, wherein the game further includes sets of playing cards, each set corresponding to various game skill levels.
 4. A game comprising a game environment; a move generator associated with the game comprising numbers, mathematical operators, mathematical operations, variables, and variable values; wherein the move comprises any change in the game environment.
 5. A method for moving of a game token along a game travel path the method comprising: selecting mathematical expression components from the group consisting of numbers, mathematical operators, mathematical operations, variables and variable values; forming the mathematical expression components into a mathematical expression to yield a movement value; moving the game token along the game travel path according to rules of the game for the movement value.
 6. A method for producing a move in an entertainment game having a game environment, the method comprising: selecting mathematical expression components from the group consisting of numbers, mathematical operators, mathematical operations, variables and variable values; forming the mathematical expression components into a mathematical expression to yield a movement value; and implementing a move corresponding to the movement value to effect the game environment.
 7. The method of claim 6, wherein the move corresponds to changes in the game environment comprising changing position, size, shape, coloration, or pattern of a visual feature, changing pitch, duration, volume, harmony, or pattern of sound, changing pressure, temperature, or texture, changing aroma, noxiousness, intensity, duration, or changing taste, bitterness, sweetness, sourness, acidity, intensity, or duration.
 8. The method of claim 6, wherein the move corresponds to changes in the game environment comprising creating, eliminating, changing, revealing “hidden” states.
 9. The method of claim 6, wherein the move corresponds to changes in the game environment comprising providing stimulus to effect mental or emotional state of a game player. 